Their example would work in other partial views, but it does not work within the form partial view.

var username = System.Web.Security.Membership.GetUser().UserName;
var member = ApplicationContext.Services.MemberService.GetByUsername(username);

I have been using that, which is effectively the same thing, but regardless of what dependencies I include neither of those will render within the form partial view. This one doesn't allow ApplicationContext and their version:

    @if(Members.IsLoggedIn()){
   var profile = Members.GetCurrentMemberProfileModel();
   var umbracomember = Members.GetByUsername(profile.UserName);

    <h1>@umbracomember.Name</h1>
    <p>@umbracomember.GetPropertyValue<string>("bio")</p>
}

doesn't allow Members. Both will work in my controllers or other partial views, but not the form partial view.

@using BoldLogistics.Controllers
@model BoldLogistics.Models.GeneralApplicationModel

@using (Html.BeginUmbracoForm<GeneralApplicationController>("GeneralApplication"))
{
    @Html.AntiForgeryToken()
    @Html.ValidationSummary(true)

    <p>First Name</p>
    @Html.TextBoxFor(model => model.FirstName, new { placeholder = "First Name" })
    @Html.ValidationMessageFor(model => model.FirstName)

    @Html.LabelFor(model => model.LastName)
    @Html.EditorFor(model => model.LastName)
    @Html.ValidationMessageFor(model => model.LastName)

    <button class="button" id="contact-submit" type="submit"> Update</button>

}

That is what I mean, the partial view for the html form.

 @{ Html.RenderPartial("~/Views/Partials/GeneralApplicationPartial.cshtml", new GeneralApplicationModel());}

Is how I call the partial view from the template.

Sorry if my terminology of any of this is off. I am new both to Umbraco and to MVC.

That is where I am running into the problem, the form partial (or mvc partial? idk what to call it) isn't the same as a regular one, it won't allow that and still perform its intended function. There must be a way to pass the member value into the function, but I can't figure out how to do that.

That specific model is required for the form to work. That is what contains the property values/types. Without that everything breaks because there aren't definitions for the form variables.

namespace BoldLogistics.Models
{
    public class GeneralApplicationModel
    {
        [Required(ErrorMessage ="First Name is Required")]
        public string FirstName { get; set; }

        [Required(ErrorMessage ="Last Name is Required")]
        public string LastName { get; set; }        
    }
}

Without the model the error is:

For every field